# Algebra

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## Algebra

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1. Algebra 10.7 Factoring Special Products

2. Use the Patterns! First and last terms are perfect squares! 4x² + 12x + 9 (2x + 3)2 Perfect Square Trinomial! The middle term is twice the product of the square roots of the first and third terms. 4p² - 16 (2p - 4) (2p + 4) Difference of two squares (DTS)! The difference of… two squares! First and last terms are perfect squares! (2x - y)2 4x² - 4xy + y² Perfect Square Trinomial! The middle term is twice the product of the square roots of the first and third terms. The key is to recognize when you see a perfect square trinomial or a DTS!

3. Factoring Patterns! First and last terms are perfect squares! a² + 2ab + b2 (a + b)2 Perfect Square Trinomial! The middle term is twice the product of the square roots of the first and third terms. a² - b2 (a - b)(a + b) Difference of two squares (DTS)! The difference of… two squares! First and last terms are perfect squares! a² - 2ab + b² (a - b)2 Perfect Square Trinomial! The middle term is twice the product of the square roots of the first and third terms. The key is to recognize when you see a perfect square trinomial or a DTS!

4. Factor! 2x²- 18 2(x + 3)(x – 3) 2(x²- 9) DTS! (7t + ½r)(7t – ½r) 49t²- ¼r2 DTS! 81x²- 25y² (9x – 5y)(9x + 5y) DTS! 27x²- 12 3(3x + 2)(3x – 2) 3(9x²- 4) DTS!

5. Factor! -3x²- 18x - 27 -3(x + 3)2 -3(x²+ 6x + 9) Perfect Square Trinomial! (3y – 10)2 9y²- 60y + 100 Perfect Square Trinomial! 2x²- 12x + 18 2(x – 3)2 2(x²- 6x + 9) Perfect Square Trinomial! 49x²+ 84x + 36 (7x + 6)2 Perfect Square Trinomial!

6. Solve! (x – 5)2 = 0 3x²- 30x = -75 3x²- 30x + 75 = 0 x= 5 Divide each side by 3! x²- 10x + 25 = 0 Perfect Square Trinomial! (6y + 11)(6y – 11) = 0 36y²- 121 = 0 y= 11/6, -11/6 DTS! -6x²+ 8x + 14 = 0 (x )(3x ) = 0 + - 1 7 Divide each side by -2! 3x²- 4x – 7 = 0 x= -1, 7/3

7. Solve! (2x + 1)(2x – 1)= 0 4x²- 1 = 0 x= ½, -½ DTS! (7x )(x ) = 0 – – 3 1 7x²- 10x = -3 7x²- 10x + 3 = 0 x= 1, 3/7 32x²- 80x + 50 = 0 (4x – 5)2 = 0 Divide each side by 2! 16x²- 40x + 25 = 0 x= 5/4 Perfect Square Trinomial!

8. HW • P. 622-624 (#19-61, 83-93) Odds Maybe factor out instead of divide each side by GCF as it applies to Ch 11